Out of 32 cards, Mookie guessed the color correctly 18 times. What would this be as a decimal? ((Type in 4 digits after the decimal))

The perimeter of the shaded region is 135 in.

Given, a triangle ABC in which K, L & M are the mid-points of the sides AB, BC, AC.

Also, the perimeter of the triangle ABC is 108 in.

Now, using the mid-point theorem, we get

KL = 1/2(AC)

LM = 1/2(AB)

KM = 1/2(BC)

Now, the perimeter of the shaded region is,

Perimeter of 3 small triangles + Perimeter of triangle KLM

Perimeter of 3 small triangles = (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4)

Perimeter of triangle KLM = AB/2 + BC/2 + AC/2

Perimeter of the shaded region = (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/2 + BC/2 + AC/2)

Perimeter of the shaded region = 5/4(AB + BC + AC)

As, we know that AB + BC + AC = 108 in

Perimeter of the shaded region = 5/4×108

Perimeter of the shaded region = 135 in

Hence, the perimeter of the shaded region is 135 in.

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Answer:

Asymptote: x= -8
Two points: (-7,0) and (-6,-1)

Step-by-step explanation:

1. Convert log form to exponential form.
y = -2log_4(x+8)
-y/2=log_4(x+8)
4^(-y/2)=x+8
x=4^(-y/2)-8

Note: from here, you can choose to find the inverse of the graph, solve f(x)^-1, and then revert the x and y coordinates to find the f(x) (but I won't be going over that because the question is not asking for the inverse).

2. Make a table by plugging in points.
At this point, all you need to do is to plug in y-values into the equation: x=4^(-y/2)-8
If we plug in y as 0, we get x as -7, and plug in y as -1, we get x as -6, so (-7,0) and (-6,-1) will be your two points.

3. Find the asymptote

An asymptote is a line in which the log function will approach infinitely close to, but never touch. Same deal, we can try to plug in more numbers into our graph -- y as 1 and we will get x as -15/2 (-7.5); y as 3 and we will get x as -63/8 (-7.875); y as 5 and we will get x as-255/32 (-7.96875). At this point, it's pretty clear that our graph is approaching -8. Hence, x= -8
We use vertical asymptote (x=) when graphing log and we use horizontal asymptote (y=) when graphing exponential.

The vertical asymptote is x = -8.

One point on the graph is (-7, 0).

Another point on the graph is (-6, -1).

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To graph the function [tex]f(x) =-2 \log _{4}(x+8),[/tex]

we need to first find the vertical asymptote, which is the value of x that makes the argument of the logarithm equal to zero.

x + 8 = 0

x = -8

So the vertical asymptote is x = -8.

Next, we can choose two integer values of x and find their corresponding values of f(x).

Let's choose x = -7 and x = -6.

When x = -7:

[tex]f(-7) = -2 \log _{4}(-7+8) = -2 \log _{4}(1) = 0[/tex]

So one point on the graph is (-7, 0).

When x = -6:

[tex]f(-6) = -2 \log _{4}(-6+8) = -2 \log _{4}(2) = -2(1/2) = -1[/tex]

So another point on the graph is (-6, -1).

Now we can plot the points and draw the vertical asymptote at x = -8.

Thus,

The vertical asymptote is x = -8.

One point on the graph is (-7, 0).

Another point on the graph is (-6, -1).

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Probability that first two babies born are boys is 0.23

Number of Mothers to be received ultrasound = 14

Number of mother giving birth to girl = 7

Number of mother giving birth to boy = 14 - 7 = 7

P(giving birth to girl) = P(G) = 7 / 14 = 0.5

P(giving birth to boy) = P(B) = 7 / 14 = 0.5

Probability that the first two babies that are born happen to be boys =

favorable outcome / total outcome

here, favorable outcome = ⁷C₂

Total outcome = ¹⁴C₂

Required probability = ⁷C₂ / ¹⁴C₂

= (7×6 / 2×1) / (14×13 / 2×1)

= 7×6/14×13

= 42 / 182

=0.23

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The radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].

How to find volume of the cone?

Given

metal radius = R = 20

cone base radius = r

cone height = h

First, we can use Pythagoras theorem

R^2 = r^2 + h^2

r^2 = R^2 - h^2

r^2 = 400 - h^2

Then, we use volume of cone formula

V = 1/3[tex]\pi[/tex] * r^2 * h

V = 1/3[tex]\pi[/tex] * (400 - h^2) * h

V = 1/3[tex]\pi[/tex] * 400h - h^3

To get maximum volume of cone, V'(h) must be 0. So,

1/3[tex]\pi[/tex] * 400 - 3h^2 = 0

400 - 3h^2 = 0

3h^2 = 400

h^2 = 400/3

h = [tex]\frac{20}{\sqrt{3}}[/tex] or 11.55

Next, we find the r with substitution method. So,

r^2 = 400 -  ([tex]\frac{20}{\sqrt{3}}[/tex]    )^2

r^2 = 400 - [tex]\frac{400}{3}[/tex]

r^2 = [tex]\frac{800}{3}[/tex]

r = [tex]\frac{20\sqrt{2}}{\sqrt{3}}[/tex] or 16.33

Now, we can get maximum volume of cone.

V = 1/3[tex]\pi[/tex] *  16.33^2 * 11.55

V = 1,026.67[tex]\pi[/tex]

Thus, the radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].

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Using the percentage of money the group gave out to the youth program, the amount of money the group raised is 6200 dollars.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

The group gives 50% of the money they raised to youth programs. This year the team gave $3,100 to youth programs.

Therefore, the amount of money the group raised can be calculated as follows:

let

x = amount of money raised by the group

Hence,

50% of x = 3100

50 / 100 × x = 3100

50x / 100 = 3100

cross multiply

50x = 3100 × 100

50x = 310000

divide both sides by 50

50x / 50 = 310000 / 50

x = 6200

Therefore, the group raised 6200 dollars this year.

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The coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)

The end points of the line segment = (-9, -10) and (1, 5)

The partition ratio = 2 : 3

According to the partition rule

The x coordinate of the point = [tex]x_1+\frac{A(x_2-x_1)}{A+B}[/tex]

A = 2

B = 3

Substitute the values in the equation

The x coordinate of the point = -9 + [2(1--9) / 2+3]

= -9 + [2×10 / 5]

= -9 + [20/5]

= -9 + 4

= -5

Similarly,

The y coordinate of the point = [tex]y_1+\frac{A(y_2-y_1)}{A+B}[/tex]

= -10+[2(5--10)/2+3]

= -10+[2×15/5]

= -10+[30/5]

= -10 + 6

= -4

Hence, the coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)

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The equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3

The total amount that they have to spend on parking and admission = $89.50

The parking cost = $7.75

The ticket cost including tax = $27.25

Consider the number of people who can go to amusement park as p

Then the equation will be

7.75 + 27.25p = 89.50

Subtract both side of the equation by 7.75

27.25p + 7.75 - 7.75 = 89.50 - 7.75

27.25p = 81.75

Divide both side of the equation by 27.25

27.25p / 27.25 = 81.75 / 27.25

p = 3

Hence, the equation which can be used to determine p is 7.75 + 27.25p = 89.50, then the number of people who can go to the amusement park is 3

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Answer:

16.80

Step-by-step explanation:

The ratio is 1:5.60. Where 1 is the amount of friends and 5.60 is the amount owed. Since there are 3 friends, multiply 5.60 by 3.

Answer: 16.8

Step-by-step explanation: basically multiply 5.60 by 3 (5.60 x 3 = 16.8) or add 5.60 3 times (5.60 + 5.60 + 5.60 = 16.8)

Using the concepts of equilateral triangle, we got that  2.113 is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles.

Firstly we find the side length of equilateral triangle , G is the midpoint of side FE.

Let GE=x, since G is the midpoint due to that DE=GB.

So, using basic trigonometry=DG^GB=x√3.

Thus DB=2x√3.

Since DB is the diagonal of ABCD, it has length 10√2 Then we can set up the equation 2x√3=10√2. So the side length of the triangle is

2x=(10√2)/√3.

Now look at the diagonal AC it is made up of twice the diagonal of the small square plus the side length of the triangle. Let the side length of the small square be y:

Let the side length of the small square be y:

AC=y√2 + [(10√2)/√3]+y√2=10√2.

Solving  for y:

=>y√2+y√2 + (10√2√3)/3=10√2

=>y√2+y√2 + (10√6)/3=10√2

=> [3y√2+3y√2 + (10√6)] /3=10√2

=>6y√2+10√6=30√2

=>6y√2 = 30√2-10√6

=>y√2 = (30√2-10√6)/6

=>y = (30√2-10√6)/6√2

=>y = (60-20√3)/12

=>y= 5(3−√3)3  or 2.113

Hence, inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles is to be 2.113.

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Answer:

7x 3,012=7(__3000__+__12_) = 21084

The probability that every even number appears at least once before the first occurrence of an odd number is  [tex]\frac{1}{20}[/tex]

Take  [tex]A_{k}[/tex]  - the event that odd number appeared on the k-th throw,  B  - every even number appeared at least once.

Let’s find  P(B|[tex]A_{k}[/tex]) . Note that this probability is 0 for  k∈{1,2,3}  as you need  k≥4  to place all distinct even numbers before the odd one.

Now for  k≥4  we need to use the formula of inclusions and exclusions:  P(B¯|[tex]A_{k}[/tex])=P(C2+C4+C6|[tex]A_{k}[/tex])=

=P(C2|[tex]A_{k}[/tex])+P(C4|[tex]A_{k}[/tex])+P(C6|[tex]A_{k}[/tex])−P(C2C4|[tex]A_{k}[/tex])−P(C2C6|[tex]A_{k}[/tex])−P(C4C6|[tex]A_{k}[/tex])  where  Ci  is the event that the dice i is missing.

These probabilities are:

P(Ci/[tex]A_{k}[/tex])=[tex](\frac{2}{3} )^{k-1}[/tex]

P(CiCj|[tex]A_{k}[/tex])=[tex](\frac{1}{3} )^{k-1}[/tex]

So

P(B|[tex]A_{k}[/tex])=1–P(B¯|[tex]A_{k}[/tex])=1−3⋅[tex](\frac{2}{3} )^{k-1}[/tex]+3[tex](\frac{2}{3} )^{k-1}[/tex].= 1 − [tex]\frac{9}{2}[/tex].[tex](\frac{2}{3} )^{k}[/tex]+9[tex](\frac{1}{3} )^{k}[/tex]

Now as  P([tex]A_{k}[/tex])= [tex]\frac{1}{2^{k} }[/tex]we conclude that

P(B) = ∞∑k=4P(B/[tex]A_{k}[/tex])P([tex]A_{k}[/tex])=  ∞∑k=4([tex](\frac{1}{2} )^{k}[/tex]−[tex]\frac{9}{2}[/tex][tex](\frac{1}{3} )^{k}[/tex]+9.[tex](\frac{1}{6} )^{k}[/tex])=

=[tex]\frac{\frac{1}{16} }{\frac{1}{2} }[/tex]−[tex]\frac{\frac{1}{18} }{\frac{2}{3} }[/tex]+[tex]\frac{\frac{1}{144} }{\frac{5}{6} }[/tex] = [tex]\frac{1}{8}[/tex] -[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{120}[/tex] =[tex]\frac{6}{120}[/tex] = [tex]\frac{1}{20}[/tex]

the probability that every even number appears at least once before the first occurrence of an odd number is  [tex]\frac{1}{20}[/tex]

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Answer:

it is 20

Step-by-step explanation:

use the formula

hope i helped

The remainder of the division of the given polynomial by (x - 3) is 966.

From the question, we have

f(x) = 4x^5 - x - 3

The remainder of the division is the f(x) at x= 3

f(3) = 4*3^5 - 3 - 3

=972-6

=966

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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1(3x+9)/3 = -3x + 11,  3x/3 + 9/3, x + 3, 8 and 2 should be entered in each blank space respectively

Given: the algebraic equation, 4(3x+9)/12 = -3x + 11

4(3x+9)/12 = -3x + 11      

Divide the Right-Hand Side (RHS) by 4 to get:

1(3x+9)/3 = -3x + 11

Then, on the RHS divide 3x and 9 separately by 3:

3x/3 + 9/3  = -3x + 11

x + 3  = -3x + 11

Take -3x to the Left and take 3 to the right (Note that, this will change their signs):

x + 3 + 3x = 11

x+3x = 11-3

Add/subtract like terms:

4x = 8

Divide both sides by 4:

x = 8/4

x = 2

Therefore, 1(3x+9)/3 = -3x + 11,  3x/3 + 9/3, x + 3, 8 and 2 should be entered in each blank space accordingly. The solution of the equation is x =2

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Answer:

For points earned (p), the button should be on the left, and for questions correct (q), its on the right.

Step-by-step explanation:

me not know how to speak English!

In the given equation p = 5q, p is the dependent variable and g is the independent variable.

Given that Tatiana earns 5 points for each question she answers.

So, the equation is p = 5q

The above equation explains that for every question she answers, she earns 5 points. That means answering questions which is "q" is an independent variable as it is not depending on any other factor.

The points earned which is "p", is completely depending on answering questions, so the "p" which is points earned is a dependent variable.

From the above explanation, we can conclude that p is dependent variable and q is independent variable.

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The area of the shaded portion of the circular disc is  112.255 cm².

A circle is a bounded object in which points from its center to its circumference is equidistant.

The area of the shaded portion is the difference between the area of the circular disc and the area of the circular hole.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius

Area of the circular disc = 3.14 x 6²

Area of the circular disc = 3.14 x 36

Area of the circular disc = 113.04 cm²

Area of the circular hole = 3.14 x 0.5²

Area of the circular hole = 3.14 x 0.25

Area of the circular hole = 0.785 cm²

Area of the shaded portion = area of the circular disc - area of the circular hole

Area of the shaded portion = 113.04 cm² -  0.785 cm²

Area of the shaded portion = 112.255 cm²

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The statements that is true are "6 + 3 = 9 and 4 x 4 = 16" , the true statement is (2) .

In the question ,

four statements are given ,

we need to find which statement is true ,

Option(1) ,

if 6 > 10, then 8 x 3 = 24

we know , that 10 > 6 , but it is given that 6 > 10 ,

hence the statement is false  .

Option(2)

6 + 3 = 9 and 4 x 4 = 16

we know , that 6+3=9 and 4×4=16

so , the statement is true .

Option(3)

if 6 x 3 = 18 then 4+8=20

we know , that 4+8 = 12 , but it is given that 4+8=20

So , the statement is false ,

Option(4)

5x3=15 or 7+5 = 20

we know , that 7+5 = 12 , but it is given that 7+5=20

So , the statement is false .

Therefore , The statements that is true are "6 + 3 = 9 and 4 x 4 = 16" , the true statement is (2) .

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The cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00

Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase

Let n-----> the number of sodas

C(n) -----> the total cost

we know that

The total cost is equal to the number of sodas multiplied by the cost of one soda minus $0.50 of the coupon

so

C(n) = 0.75n – 0.5

For n=10 sodas

substitute the value of n in the equation

C(10) = 0.75(10) – 0.5

7.5 - 0.5

= 7

Therefore, the cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00

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X= 1

First you subtract 6 from both sides to get

2x=2

Then you divide by 2 to get 1

x=1

Answer:

Each interior angle of a regular polygon is 174°

To find The number of sides of the polygon.

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the polygon)

Now, the sum of an interior angle and an exterior angle of a regular polygon is always equal to 180°.

So, the exterior angle of the given regular polygon :

= (Sum of an interior angle and an exterior angle) - (An interior angle)

= 180° - 174°

= 6°

Let, the number of sides of the regular polygon = n

Now, the value of an exterior angle of a regular polygon = (360° / Number of sides)

So, the exterior angle of the given regular polygon :

= (360°/n)

By, comparing the two values of an exterior angle of the given regular polygon, we get :

360/n = 6

n × 6 = 360

n = 360/6

n = 60

Number of sides of the regular polygon = n = 60

(This will be considered the final result.)

Hence, the number of sides of the regular polygon is 60.

if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases

1. Critical Value: The value of the statistic for which the test just rejects the null hypothesis at the given significance level.

2. Power of the Test: The probability that the test correctly rejects the null hypothesis when the alternative is true.

3. Significance Level: The prescribed rejection probability of a statistical hypothesis test when the null hypothesis is true.

4. Size of the test: The probability that the test incorrectly rejects the null hypothesis when it is true.

if n decreases then the value of level of significance of each samples [tex]\alpha[/tex] decreases and hence 1- [tex]\alpha[/tex] increases which are called the rejection of test sample increases

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Answer:3 1/2 hours

Step-by-step explanation: 5 2/5 - 1 1/4 -1 1/2= 3 1/2

The sun's angle of elevation when a 47-foot mast casts a 14-foot shadow 73.4127

At the foot of the mast, place the 90 degree (right) angle of a right triangle. When the sun hits the mast, it casts a 47-foot shadow. Consider the mask's height to be on the "opposite side" of the elevation angle, and this shadow to be on the "adjacent side."

The "tangent" trig function includes the following variables:

Tan = (opposite side) (elevation angle) (adjacent side).

In this case, tan (angle of elevation) equals opposing side / adj opposing side.

is used for

radians, or tan (angle of elevation)

= 47/14 = 3.3571

3.3571 is equal to 73.4127 degree.

The angle of elevation of the sun when a 47-ft mast casts a 14 ft

shadow 73.4127 degree

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Answer: No, the marketing manager was not correct in his claim.

We are given that in a survey of 1005 adult Americans, 46.6% indicated that they were somewhat interested or very interested in having web access in their cars.

Suppose that the marketing manager of a car manufacturer claims that the 46.6% is based only on a sample and that 46.6% is close to half, so there is no reason to believe that the proportion of all adult Americans who want car web access is less than 0.50.

Let p = population proportion of all adult Americans who want car web access.

SO, Null Hypothesis,  : p  50%   {means that the proportion of all adult Americans who want car web access is more than or equal to 0.50}

Alternate Hypothesis,  : p < 50%  {means that the proportion of all adult Americans who want car web access is less than 0.50}

The test statistics that will be used here are One-sample z-proportion statistics;

               T.S.  =    ~ N(0,1)

where = sample proportion of Americans who indicated that they were somewhat interested or very interested in having web access in their cars =  46.6%

           n = sample of Americans = 1005

So, test statistics  =  

                              =  -2.161

Since in the question we are not given the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives the critical value of -1.6449 for the left-tailed test. Since our test statistics are less than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Step-by-step explanation:

The simplified expression representing (−8x²−5x+8)−(−6x²+3x−3) is given as follows:

14x² - 8x + 11.

The expression for this problem is presented as follows:

(−8x²−5x+8) − (−6x²+3x−3).

The first step towards simplifying the expression is removing the negative signal from the expression, inverting the signal of each term inside the second parenthesis, hence:

(−8x²−5x+8) − (−6x²+3x−3) = 8x² - 5x + 8 + 6x² - 3x + 3.

(the first parenthesis can be removed with no changes as there is not any signal in front of it).

Then the like terms, which are the terms with the same variable and same exponent, are added, adding the coefficients and keeping the variables and exponents, as follows:

The simplified expression is obtained by these three additions of the like terms above, hence:

14x² - 8x + 11.

The problem is incomplete, and it asks for us to simplify the given expression.

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From the graph the turning points are 4 i.e. (-1.467,17.765), (0,0),  (1.251,6.665), (2.616,-7.472), global maximum is (-1.467,17.765), global  minimum is (2.616,-7.472), local maximum is (0,0) and local maximum is (1.251,6.665).

In the given function, we have to  graph the function, then use the graph to determine the number of turning points, global maximums and minimums, and local maximums and minimums that are not global.

The given function is h(x) = x^2(x − 3)(x + 2) (x - 2).

The graph of the given function is below:

As we know that

A local minimum or maximum is represented by each turning point. A turning point may occasionally be the peak or trough of the entire graph. In these situations, we argue that a global maximum or global minimum marks the turning moment.

The output at the greatest or lowest point of the function is referred to as a global maximum or global minimum.

So the terning point of the given function is 4 i.e. (-1.467,17.765), (0,0),  (1.251,6.665), (2.616,-7.472).

Global Maximum = (-1.467,17.765)

Global Minimum = (2.616,-7.472)

Local Maximum = (0,0)

Local Maximum = (1.251,6.665)

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The linear equations that can satisfy the values given in tabular form are

How to form line equation using values given in tabular form?

A line equation is of the form y = mx + b where x and y are the coordinate values, m is the slope of the line and b is the y intercept.

Follow these steps to find the line equation:

According to the given data:

Table I)

Standard form: t = md + b

Slope: m = [tex]\frac{16 - 11}{1 - 0}[/tex] = 5

y-intercept: t = 5d + b

Substituting (d, t) = (1, 16) as given in the table

16 = 5x(1) + b

∴ b = 11

Hence linear equation in terms of d and t is t = 5d +11

Similarly, for Table II)

Standard form: c = mr + b

Slope: m = [tex]\frac{2 - 1}{-0.6 + 2.1}[/tex] = [tex]\frac{2}{3}[/tex]

y-intercept: c =     (2/3)r + b

Substituting (r, c) = (-2.1, 1) as given in the table

1 = 2/3 x (-2.1) + b

∴ b = 2.4

Hence linear equation in terms of r and c is c =  [tex]\frac{2}{3}[/tex] r + 2.4

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Answer: decay

Step-by-step explanation: decay is when the input is less than 1 and greater than 0. 0.75 falls in between these numbers

the tell-tale factor is the value inside the parenthesis, if that's less than 1 is Decay, if more than 1 is Growth

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2.5\\ r=rate\to \text{\LARGE 28\%}\to \frac{28}{100}\dotfill &0.28\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=2.5(1 - 0.28)^{x} \implies A = 2.5(0.72)^x\hspace{5em}y= 2.5(0.72)^x[/tex]

The square root of 92 lies between 9 and 10.

According to the question,

We have the following information:

Square root of 92

Now, we have to find the two integers between which its square root lie.

So, we will first find the perfect squares of positive integers to get an idea where the square root of 92 lies.

Perfect squares are given below:

1 = 1

2 = 4

3 = 9

4 = 16

5 = 25

6 = 36

7 = 49

8 = 64

9 = 81

10 = 100

Now, the square of 10 is greater than 92 and square of 9 is less than 92. So, it will lie between these two integers.

Hence, the square root of 92 lies between 9 and 10.

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The common difference 9 will make 5, x, y, 32 an arithmetic sequence of 5, 14, 23, 32.

It is given that the arithmetic sequence is

5, x, y, 32

We know that for any arithmetic sequence the term aₙ is

aₙ = a + (n - 1)d

where,

a = first term

n = order of the value in the sequence

Since x is the second term

x = 5 + (2 - 1)d

or, x = 5 + d

Similarly,

y = 5 + 2d

32 = 5 + 3d

or, 3d = 27

or, d = 9

Hence, x = 14

y = 5 + 18

= 23

Hence, the common difference is 9

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